Abstract
AbstractWe construct an integrated multi‐period inventory–production–distribution replenishment plan for three‐stage supply chains. The supply chain maintains close relationships with a small group of suppliers, and the nature of the products (bulk, chemical, etc.) makes it more economical to rely upon a direct shipment, full‐truck load distribution policy between supply chain nodes. In this paper, we formulate the problem as an integer linear program that proves challenging to solve due to the general integer variables associated with the distribution requirements. We propose new families of valid cover inequalities, and we derive a practical closed‐form expression for generating them, upon the determination of a single parameter. We study their performances through benchmarking several branch‐and‐bound and branch‐and‐cut approaches. Computational testing is performed using a large‐scale planning problem faced by a North American company.
Highlights
We consider a general integer linear program with binary and general integer variables that is of the form: min cT x subject to Ax ≥ b x≥0 (1)
mixed integer linear programs (MILP) with general integer variables are very common in industrial applications
This study is motivated by the problem faced by a chemical supply chain
Summary
We consider a general integer linear program with binary and general integer variables that is of the form: min cT x subject to Ax ≥ b x≥0 (1). We propose a new closed-form expression to derive valid cover inequalities for the knapsack constraints described above This expression depends on a single parameter, so that the associated cuts can be obtained directly, without having to implement a recursive generating procedure. The valid inequalities derived in this paper for the type of knapsack constraints in X are thereafter referred to as binary-integer cover inequalities The advantage of these cuts over other families of cuts for the specific application problem is that they are easy to generate and seem to provide a bigger lower bound improvement.
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